A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

Pablo Manuel Berná and Diego Mondéjar
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Pablo Manuel Berná: Departamento de Matemática Aplicada y Estadística, Facultad de Ciencias Económicas y Empresariales, Universidad San Pablo-CEU, CEU Universities, 28003 Madrid, Spain
Diego Mondéjar: Departamento de Matemática Aplicada y Estadística, Facultad de Ciencias Económicas y Empresariales, Universidad San Pablo-CEU, CEU Universities, 28003 Madrid, Spain

Mathematics, 2021, vol. 9, issue 15, 1-14

Abstract: In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco.

Keywords: greedy algorithm; nonlinear approximation; bases; Banach spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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